Influence of tachyonic instability on the Schwinger effect in Higgs inflation model

Abstract

We investigate the influence of the tachyonic instability on the Schwinger effect in Higgs inflation model.In this work we identify the standard horizon scale $ k_{H}=aH $ and the tachyonic instability $ k_{H}=aH|\zeta| , \zeta=\frac{{I}^{\prime}\left(\phi\right)\dot{\phi}}{H} $.This is the horizon scale in which the given Fourier begins to become tachyonically unstable.Influence of this scale appears by vanishing electromagnetic field energy density and energy density of created charged particles due to the Schwinger effect at the very beginning of inflation but does not alter conclusions of our previous work in Refs.\cite{Kamarpour:2022,Kamarpour:2023-I}.We use two coupling functions to break conformal invariance of maxwell action.The simplest coupling function $ I\left(\phi\right)=\chi_{1}\frac{\phi}{M_{p}} $ and a curvature based coupling function $ I\left(\phi\right)= 12\chi_{1}e^{\left(\sqrt{\frac{2}{3}}\frac{\phi}{M_{p}}\right)}\left[\frac{1}{3M_{p}^{2}}\left(4V\left(\phi\right)\right)+\frac{\sqrt{2}}{\sqrt{3}M_{p}}\left(\frac{dV}{d\phi}\right)\right] $ where $V\left(\phi\right) $ is the potential of Higgs inflation in Refs.\cite{Kamarpour:2022,Kamarpour:2023-I}.In fact, we find that only at the very beginning of inflation both energy densities of electromagnetic field and created charged particles vanish due to effect of tachyoinc instability.